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123
GATE IN 2023 | Question: 43
Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The sample standard deviation of the measurement ___________is $\mathrm{kg}$ (rounded off to two decimal places).
Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The ...
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127
GATE IN 2023 | Question: 47
Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded off to one decimal place).
Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded ...
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129
GATE IN 2023 | Question: 49
The opamps in the circuit are ideal. The input signals are $\mathrm{V}_{\mathrm{S} 1}=3+0.10 \sin (300 t) ~ \mathrm{V} \text { and } \mathrm{V}_{\mathrm{S} 2}=-2+0.11 \sin (300 t) ~ \mathrm{V}$ The average value of the voltage $V_0$ is_____________$\text{V}$ (rounded off to two decimal places).
The opamps in the circuit are ideal. The input signals are$$\mathrm{V}_{\mathrm{S} 1}=3+0.10 \sin (300 t) ~ \mathrm{V} \text { and } \mathrm{V}_{\mathrm{S} 2}=-2+0.11 \si...
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132
GATE IN 2023 | Question: 52
In the circuit shown, assuming an ideal opamp, the value of the output voltage $\mathrm{V}_{\mathrm{o}}=$____________$\mathrm{V}$ (rounded off to one decimal place).
In the circuit shown, assuming an ideal opamp, the value of the output voltage$\mathrm{V}_{\mathrm{o}}=$____________$\mathrm{V}$ (rounded off to one decimal place).
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133
GATE IN 2023 | Question: 53
The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha}{\beta}$ is __________ (rounded off to the nearest integer). $A=\left[\begin{array}{cc} 1 & 4 \\ -3 & \alpha \\ \beta & 6 \end{array}\right]$
The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha}{\beta}$ is __________ (rounded off to the nearest integer).$$A=\left[\begin{array}{cc}1 & 4 \\-3 &...
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139
GATE IN 2022 | Question: 4
The output of a system $y(t)$ is related to its input $x(t)$ according to the relation $y(t) = x(t) \sin (2 \pi t).$ This system is __________ Linear and time-variant Non-linear and time-invariant Linear and time-invariant Non-linear and time-variant
The output of a system $y(t)$ is related to its input $x(t)$ according to the relation $y(t) = x(t) \sin (2 \pi t).$ This system is __________Linear and time-variantNon-l...
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140
GATE IN 2022 | Question: 5
A unity-gain negative-feedback control system has a loop-gain $L(s)$ given by $L(s) = \frac{6}{s(s-5)}$ The closed-loop system is _________ Causal and stable Causal and unstable Non-causal and stable Non-causal and unstable
A unity-gain negative-feedback control system has a loop-gain $L(s)$ given by$$L(s) = \frac{6}{s(s-5)}$$The closed-loop system is _________Causal and stableCausal and uns...
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142
GATE IN 2022 | Question: 7
A Hall sensor is based on the principle of ___________ Photoelectric effect Seebeck effect Piezoelectric effect Lorentz force
A Hall sensor is based on the principle of ___________Photoelectric effectSeebeck effectPiezoelectric effectLorentz force
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145
GATE IN 2022 | Question: 10
The resistance of a pure copper wire of length $10 \; \text{cm}$ and diameter $1 \; \text{mm}$ is to be measured. The most suitable method from amongst the choices given below is _________ Two wire method Three wire method Four wire method Ellipsometry
The resistance of a pure copper wire of length $10 \; \text{cm}$ and diameter $1 \; \text{mm}$ is to be measured. The most suitable method from amongst the choices given ...
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146
GATE IN 2022 | Question: 11
The logic block shown has an output $F$ given by ________ $A + B$ $A \cdot \overline{B}$ $A + \overline{B}$ $\overline{B}$
The logic block shown has an output $F$ given by ________$A + B$$A \cdot \overline{B}$$A + \overline{B}$$\overline{B}$
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147
GATE IN 2022 | Question: 12
In which of the following bridge(s) is the balancing condition frequency-independent? Maxwell bridge Wien bridge Schering bridge Wheatstone bridge
In which of the following bridge(s) is the balancing condition frequency-independent?Maxwell bridgeWien bridgeSchering bridgeWheatstone bridge
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149
GATE IN 2022 | Question: 15
An analog-to-digital converter with resolution $0.01 \; \text{V}$ converts analog signals between $0 \; \text{V}$ to $+10 \; \text{V}$ to an unsigned binary output. The minimum number of bits (in integer) in the output is _________
An analog-to-digital converter with resolution $0.01 \; \text{V}$ converts analog signals between $0 \; \text{V}$ to $+10 \; \text{V}$ to an unsigned binary output. The m...
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150
GATE IN 2022 | Question: 16
Consider $24$ voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at $12 \; \text{kHz}$ and represented by an $8$-bit word, the bit-duration (in microseconds) is __________ (round off to two decimal places)
Consider $24$ voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at $12 \; \text{kHz}$ and represented by an $8$-...
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152
GATE IN 2022 | Question: 18
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
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153
GATE IN 2022 | Question: 19
A $\text{440 V, 8 kW, 4-pole, 50 Hz,}$ star-connected induction motor has a full load slip of $0.04.$ The rotor speed (in rpm) at full load is ________ (round off to one decimal place)
A $\text{440 V, 8 kW, 4-pole, 50 Hz,}$ star-connected induction motor has a full load slip of $0.04.$ The rotor speed (in rpm) at full load is ________ (round off to one ...
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154
GATE IN 2022 | Question: 20
The transfer function of a system is: $\frac{(s+1)(s+3)}{(s+5)(s+7)(s+9)}$ In the state-space representation of the system, the minimum number of state variables (in integer) necessary is _________
The transfer function of a system is:$$\frac{(s+1)(s+3)}{(s+5)(s+7)(s+9)}$$In the state-space representation of the system, the minimum number of state variables (in inte...
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156
GATE IN 2022 | Question: 22
A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are red is ____________ (round off to two decimal places)
A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are re...
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157
GATE IN 2022 | Question: 23
In the bandpass filter circuit shown, $R_{0} = 50\; \Omega, L_{0} = 1 \; \text{mH,} \; C_{0} = 10 \; \text{nF.}$ The $\text{Q}$ factor of the filter is _________ (round off to two decimal places)
In the bandpass filter circuit shown, $R_{0} = 50\; \Omega, L_{0} = 1 \; \text{mH,} \; C_{0} = 10 \; \text{nF.}$ The $\text{Q}$ factor of the filter is _________ (round o...
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158
GATE IN 2022 | Question: 24
The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value of the next approximation $x_{1}$ is ________ (round off to two decimal places)
The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value...
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